Which one of the following is the amount of heat gi ven up when 20g of steam at 100°C is condensed and cooled to 20°C?

1. Fundamental Concepts of Heat and Temperature (basic)

To master thermal physics, we must first distinguish between two terms often used interchangeably in daily life: heat and temperature. Heat represents the total molecular movement (kinetic energy) of particles within a substance. It is a form of energy that flows from a warmer object to a cooler one. On the other hand, temperature is the measurement in degrees of how hot or cold a thing or place is Fundamentals of Physical Geography, NCERT Class XI, Solar Radiation, Heat Balance and Temperature, p.70. Think of heat as the total quantity of thermal energy, while temperature is the intensity or level of that energy.

In the context of our planet, the interaction of solar radiation (insolation) with the atmosphere and the Earth's surface creates heat. This heat is not distributed uniformly. For instance, as the sun moves apparently northwards, a "heat belt" shifts, causing temperatures to rise significantly in the Indian subcontinent between March and May Contemporary India-I, NCERT Class IX, Climate, p.30. While temperatures in the Deccan Plateau might reach 38°C in March, the northwestern parts of India can soar to 48°C by May India Physical Environment, NCERT Class XI, Climate, p.34. These recordings measure the intensity (temperature), but the actual energy required to raise these temperatures across such vast landmasses involves massive amounts of heat transfer.

Crucially, heat exchange can occur in two distinct ways: sensible heat and latent heat.

• Sensible Heat: This is the heat you can "sense" or measure with a thermometer because it causes a change in temperature. For example, warming water from 20°C to 100°C involves sensible heat.
• Latent Heat: Also known as "hidden heat," this is energy used to change the state of a substance (like turning ice to water or water to steam) without changing its temperature. During a phase change, such as steam condensing into water at 100°C, a significant amount of latent heat is released even though the thermometer stays fixed at 100°C.

Sources: Fundamentals of Physical Geography, NCERT Class XI, Solar Radiation, Heat Balance and Temperature, p.70; Contemporary India-I, NCERT Class IX, Climate, p.30; India Physical Environment, NCERT Class XI, Climate, p.34

2. Specific Heat Capacity and Sensible Heat (basic)

When we talk about heat in the atmosphere or the oceans, we often distinguish between heat that changes temperature and heat that changes the physical state of a substance. Sensible Heat is the energy that causes a change in the temperature of an object or substance that can be "sensed" or measured by a thermometer. If you heat a pot of water and the temperature rises from 20°C to 30°C, you are adding sensible heat. This is distinct from latent heat, which we will explore later, where heat is absorbed or released during a phase change (like ice melting) without any change in temperature.

The amount of sensible heat required to change a substance's temperature depends on its Specific Heat Capacity. This is defined as the amount of heat energy required to raise the temperature of one unit of mass (usually 1 gram or 1 kilogram) by 1°C. Think of it as a substance's "thermal stubbornness." Substances with a high specific heat capacity are very resistant to temperature changes; they require a vast amount of energy to warm up and, conversely, take a long time to cool down. In the context of our planet, water is the champion of specific heat.

As noted in Physical Geography by PMF IAS, Horizontal Distribution of Temperature, p.286, the specific heat of water is about 2.5 times higher than that of landmasses. This disparity is a fundamental driver of our global climate. Because water bodies act as massive heat reservoirs, they regulate the temperature of nearby coastal regions, preventing the extreme temperature swings seen in mid-continental areas. Furthermore, this stability is crucial for life; because water temperatures change much less rapidly than air, aquatic organisms live in a relatively stable thermal environment Environment, Shankar IAS Academy, Aquatic Ecosystem, p.35.

To calculate the amount of sensible heat (Q) involved in a temperature change, we use the formula: Q = m × c × ΔT, where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. For instance, if you have 20g of water cooling from 100°C to 20°C, the sensible heat released is calculated as 20g × 1 cal/g°C × 80°C = 1,600 calories Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.295.

Sources: Physical Geography by PMF IAS, Horizontal Distribution of Temperature, p.286; Environment, Shankar IAS Academy, Aquatic Ecosystem, p.35; Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.295

3. Latent Heat and Phase Transitions (intermediate)

In our journey through thermal physics, we often think of "heat" as something that always changes the temperature of an object. However, Latent Heat is a fascinating exception. It is the energy absorbed or released by a substance during a change in its physical state—such as melting or boiling—that occurs without any change in its temperature. The word "latent" comes from Latin meaning "hidden"; this heat is hidden because your thermometer won't show a rise in degrees while the phase transition is happening Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.294.

To understand why this happens, we must look at the molecular level. Normally, adding heat increases the kinetic energy of molecules, which we measure as a rise in temperature. But during a phase change, the energy is instead used to overcome the attractive forces (bonds) between molecules. For instance, when ice at 0°C melts into water, it stays at 0°C until every crystal is gone because the energy is busy breaking the solid lattice. We call this the Latent Heat of Fusion. Conversely, when water turns to steam, it absorbs the Latent Heat of Vaporization Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.295.

This concept is the engine behind many geographical phenomena. When water vapor in the atmosphere condenses into clouds, it releases that "stored" latent heat back into the surrounding air. This is known as the Latent Heat of Condensation. This release of energy is why a rising moist air parcel cools down more slowly than a dry one—the condensing vapor acts like an internal heater, fueling the growth of massive storm clouds and hurricanes Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.299.

Sources: Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.294; Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.295; Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.299

4. Modes of Heat Transfer: Conduction, Convection, Radiation (intermediate)

Heat transfer is the movement of thermal energy from a higher-temperature object to a lower-temperature one. In nature, this occurs through three distinct mechanisms: Conduction, Convection, and Radiation. Understanding these is vital for UPSC, as they explain everything from why a handle gets hot to how global wind patterns form.

Conduction is the transfer of heat through direct contact. Imagine a relay race where the runners don't move, but simply pass a baton from hand to hand. In solids, particles vibrate and pass energy to their neighbors without shifting from their original positions Science-Class VII . NCERT(Revised ed 2025), Heat Transfer in Nature, p.101. Materials like metals are "good conductors" because they allow this energy to flow easily. In our atmosphere, conduction is primarily responsible for heating the very thin layer of air that is in direct contact with the Earth's surface FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Solar Radiation, Heat Balance and Temperature, p.68.

Convection differs because it involves the actual movement of the matter itself. This occurs only in fluids (liquids and gases). When a fluid is heated, it becomes less dense and rises, while cooler, denser fluid sinks to take its place, creating a "convection cell" Physical Geography by PMF IAS, Chapter 22: Horizontal Distribution of Temperature, p.282. In Geography, we distinguish between vertical movement (Convection) and horizontal movement (Advection). While convection helps heat the troposphere vertically, advection is responsible for most of the daily weather variations in middle latitudes through the horizontal movement of air masses FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Solar Radiation, Heat Balance and Temperature, p.68.

Radiation is the only mode that requires no material medium. It travels as electromagnetic waves through the vacuum of space. This is how solar energy reaches the Earth across millions of miles of empty void Science-Class VII . NCERT(Revised ed 2025), Heat Transfer in Nature, p.97. Every object with a temperature above absolute zero emits some form of radiation.

Sources: Science-Class VII . NCERT(Revised ed 2025), Heat Transfer in Nature, p.94, 97, 101; FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.), Solar Radiation, Heat Balance and Temperature, p.68; Physical Geography by PMF IAS, Horizontal Distribution of Temperature, p.282

5. Latent Heat in Geography: Cyclones and Precipitation (exam-level)

6. Calculating Multi-stage Thermal Processes (exam-level)

In thermal physics, calculating the energy involved in complex transitions requires a multi-stage approach. When a substance undergoes a change in state (like steam turning to water) and then a change in temperature (like water cooling down), we cannot use a single formula. Instead, we must break the process into distinct segments: Phase Change and Temperature Change.

The first stage involves Latent Heat. During a phase transition—such as condensation—the temperature of the system remains constant even though energy is being released. This is because the energy change is associated with breaking or forming molecular bonds rather than changing kinetic energy. As noted in Physical Geography by PMF IAS, Vertical Distribution of Temperature, p. 295, heat is released when a gas turns into a liquid (latent heat of condensation). To calculate this, we use the formula Q₁ = m × L, where 'm' is mass and 'L' is the latent heat of vaporization/condensation (540 cal/g for water).

The second stage involves Sensible Heat. Once the steam has fully condensed into water at 100°C, any further loss of energy results in a drop in temperature. This is "sensible" because it can be sensed or measured by a thermometer. The formula used here is Q₂ = m × c × ΔT, where 'c' is the specific heat capacity (1 cal/g°C for water) and 'ΔT' is the change in temperature. The total heat released by the system is the sum of these stages: Total Heat = Q₁ + Q₂.

In a geographical context, this principle explains why saturated air parcels cool more slowly than dry ones. As water vapor condenses into clouds, it releases latent heat into the surrounding air, which offsets some of the cooling caused by expansion. This is the fundamental reason why the Wet Adiabatic Lapse Rate is lower than the Dry Adiabatic Lapse Rate Physical Geography by PMF IAS, Vertical Distribution of Temperature, p. 299.

Sources: Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.294-295; Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.299

7. Solving the Original PYQ (exam-level)

Now that you have mastered the individual building blocks of thermodynamics, this question illustrates how UPSC combines them to test your conceptual clarity. To solve this, you must apply two distinct principles you've learned: Latent Heat (energy released during a phase change) and Specific Heat (energy released during a temperature change). As discussed in Physical Geography by PMF IAS, the transition from steam to water is an exothermic process where energy is liberated even before the temperature begins to drop.

Let’s walk through the logic: First, 20g of steam at 100°C must condense into water at 100°C. Using the Latent Heat of Vaporization (540 cal/g), the heat released is 20g × 540 cal/g = 10,800 cal. Next, this 100°C water must cool down to 20°C. Using the formula for sensible heat (mass × specific heat × change in temperature), we calculate 20g × 1 cal/g°C × 80°C = 1,600 cal. Adding these two values together (10,800 + 1,600) leads us directly to the correct answer, 12,400 cal. This step-by-step approach ensures you don't overlook the massive energy exchange hidden within the phase transition.

UPSC designed the other options to catch common student errors. For instance, if a candidate forgets the latent heat phase and only calculates the cooling of water, they would get a much smaller number (1,600 cal), which isn't listed, forcing them to guess. Option (A) 10,000 cal and (B) 11,400 cal are calculation traps for those who might use an incorrect value for latent heat (like rounding 540 down to 500) or miscalculate the temperature delta. Success in these questions comes from identifying the state of the matter at every point in the process.